We theoretically predict the local density of nucleosomes on DNA brushes in a solution of molecules, which are necessary for transcription and the assembly of nucleosomes. Our theory predicts that in a confined space, DNA brushes show phase separation, where a region of relatively large nucleosomal occupancy coexists with a region of smaller nucleosomal occupancy. This phase separation is driven by an instability arising from the fact that the rate of transcription increases as the nucleosomal occupancy decreases due to the excluded volume interactions between nucleosomes and RNA polymerase during thermal diffusion and, in turn, nucleosomes are (in some cases) desorbed from DNA when RNA polymerase collides with nucleosomes during transcription. The miscibility phase diagram shows critical points, which are sensitive to the rate constants involved in transcription, the changes of interactions of DNA chain segments by assembling nucleosomes, and pressures that are applied to the brushes.

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Dilute or semidilute solutions of polyelectrolytes show below a critical temperature the phenomenon of counterion condensation. This effect leads (a) to a decrease of the effective total charge of the macroion and (b) to a counterion-induced attraction between different parts of the chain. In this paper we provide simple scaling arguments that allow one to calculate the chain size and the effective total charge as a function of temperature, solvent quality etc. Especially we show that effect (a) alone leads to a continuous reduction of the chain size with decreasing temperature. Due to a feedback-type mechanism effect (b) amplifies this collapse process in such a way that it is reminiscent of a first-order phase transition.

DNA-spools, structures in which DNA is wrapped and helically coiled onto itself or onto a protein core are ubiquitous in nature. We develop a general theory describing the non-equilibrium behavior of DNA-spools under linear tension. Two puzzling and seemingly unrelated recent experimental findings, the sudden quantized unwrapping of nucleosomes and that of DNA toroidal condensates under tension are theoretically explained and shown to be of the same origin. The study provides new insights into nucleosome and chromatin fiber stability and dynamics. as a means to efficiently pack and transport DNA into cells. In most of these ligand-DNA complexes the geometry and chemistry of the ligand surface enforces the DNA to follow a superhelical wrapping path with one or more tight turns. Remarkably, upon addition of multivalent condensing agents (like in sperm cells) or under high crowding conditions (like in virus capsids or during ψ-condensation) DNA also shows an intrinsic ability to self-organize into large toroidal spools [7].

We consider how beads can diffuse along a chain that wraps them, without becoming displaced from the chain; our proposed mechanism is analogous to the reptation of "stored length" in more familiar situations of polymer dynamics. The problem arises in the case of globular aggregates of proteins (histones) that are wound by DNA in the chromosomes of plants and animals; these beads (nucleosomes) are multiply wrapped and yet are able to reposition themselves over long distances, while remaining bound by the DNA chain.

We study the spontaneous "sliding" of histone spools (nucleosomes) along DNA as a result of thermally activated single base pair twist defects. To this end we map the system onto a suitably extended Frenkel-Kontorova model. Combining results from several recent experiments we are able to estimate the nucleosome mobility without adjustable parameters. Our model shows also how the local mobility is intimately linked to the underlying base pair sequence.

We present a theoretical analysis of the structural and mechanical properties of the 30-nm chromatin fiber. Our study is based on the two-angle model introduced by Woodcock et al. (Woodcock, C. L., S. A. Grigoryev, R. A. Horowitz, and N. Whitaker. 1993. Proc. Natl. Acad. Sci. USA. 90:9021-9025) that describes the chromatin fiber geometry in terms of the entry-exit angle of the nucleosomal DNA and the rotational setting of the neighboring nucleosomes with respect to each other. We analytically explore the different structures that arise from this building principle, and demonstrate that the geometry with the highest density is close to the one found in native chromatin fibers under physiological conditions. On the basis of this model we calculate mechanical properties of the fiber under stretching. We obtain expressions for the stress-strain characteristics that show good agreement with the results of recent stretching experiments (Cui, Y., and C. Bustamante. 2000. Proc. Natl. Acad. Sci. USA. 97:127-132) and computer simulations (Katritch, V., C. Bustamante, and W. K. Olson. 2000. J. Mol. Biol. 295:29-40), and which provide simple physical insights into correlations between the structural and elastic properties of chromatin.

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